Abstract
The Eckart-Landau-Lifshitz classical relativistic models of a viscous, heat-conducting fluid are known to lead to an infinite signal propagation velocity. This infinite value contradicts the postulate of a limiting signal velocity, equal to the velocity of light in vacuum. It is suggested that this paradox might be resolved by incorporating internal relaxation processes in the particles of the medium. It has been shown previously that in the special theory of relativity the velocity of a signal in a viscous, heat-conducting fluid with inheritance turns out to be finite. That assertion is proved in the present paper within the framework of the general theory of relativity in the approximation of a weak gravitational field.
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